Question

Part III: Bailey works part-time at a movie theater. The theater pays employees an hourly wage based on their length of employment. Write an algebraic expression that describes how much Bailey’s employer pays part-time workers.
Length of employment (months) Hourly wage (dollars/hour)
6 months                                          7.55
12 months                                        7.85
18 months                                        8.15
24 months                                        8.45

Answer 1

Given the following table showing the hourly wages of employees of a movie theater based on their length of employment.

Length of employment (months)         Hourly wage (dollars/hour)
6 months                                                          7.55
12 months                                                        7.85
18 months                                                        8.15
24 months                                                        8.45

To obtain an algebraic expression that describes how much Bailey’s employer pays part-time workers, we take two points from the table.

Recall that the equation of a linear function satisfying two points
$(x_1,y_1)$ and $(x_2,y_2)$
is given by
$\frac{y-y_1}{x-x_1} = \frac{y_2-y_1}{x_2-x_1}$

Given the two points (6, 7.55) and (12, 7.85), the algebraic expression relating the two points is given by
$\frac{y-7.55}{x-6} = \frac{7.85-7.55}{12-6} = \frac{0.3}{6} \\ \\ 6(y-7.55)=0.3(x-6) \\ \\ 6y-45.3=0.3x-1.8 \\ \\ 0.3x-6y=-43.5$

Therefore, the algebraic expression that describes how much Bailey’s employer pays part-time workers is
$0.3x-6y=-43.5$